• Open Access

Hindered diffusion of MRI contrast agents in rat brain extracellular micro-environment assessed by acquisition of dynamic T1 and T2 maps


S. Mériaux, NeuroSpin, I2BM, Commissariat à l'Énergie Atomique, Gif-sur-Yvette, France. E-mail: sebastien.meriaux@cea.fr


The knowledge of brain tissues characteristics (such as extracellular space and tortuosity) represents valuable information for the design of optimal MR probes for specific biomarkers targeting. This work proposes a methodology based on dynamic acquisition of relaxation time maps to quantify in vivo MRI contrast agent concentration after intra-cerebral injection in rat brain. It was applied to estimate the hindered diffusion in brain tissues of five contrast agents with different hydrodynamic diameters (Dotarem® ≈ 1 nm, P846 ≈ 4 nm, P792 ≈ 7 nm, P904 ≈ 22 nm and Gd-based emulsion ≈ 170 nm). In vivo apparent diffusion coefficients were compared with those estimated in an obstacle-free medium to determine brain extracellular space and tortuosity. At a 2 h imaging timescale, all contrast agents except the Gd-based emulsion exhibited significant diffusion through brain tissues, with characteristic times compatible with MR molecular imaging (<70 min to diffuse between two capillaries). In conclusion, our experiments indicate that MRI contrast agents with sizes up to 22 nm can be used to perform molecular imaging on intra-cerebral biomarkers. Our quantification methodology allows a precise estimation of apparent diffusion coefficients, which is helpful to calibrate optimal timing between contrast agent injection and MRI observation for molecular imaging studies. Copyright © 2012 John Wiley & Sons, Ltd.


Since the early days of MRI, paramagnetic (e.g. lanthanides atoms) [1, 2] and superparamagnetic (e.g. iron oxide particles) [3, 4] contrast agents have been introduced to enhance the contrast of specific structures. More recently, the increase in signal-to-noise ratio provided by innovative MRI instrumentation has opened the way to the development of new contrast agents dedicated to molecular imaging applications [5, 6], for which MRI sensitivity is one of the main challenges to be overcome. Considering the low concentration of biomarkers and the specific affinity of the functionalized probe with its target, one has to reach at least the nanomolar scale. To achieve this nanomolar detection threshold, several strategies seeking to significantly enhance contrast agent relaxivities (r1 and r2) have been proposed, often leading to high molecular weight particles and consequently high hydrodynamic diameters (dH): 20–30 nm for dendrimers [7]; 20–100 nm for ultrasmall superparamagnetic iron oxide (USPIO) nanoparticles [8]; and up to 200 nm for liposomes or emulsions incorporating more than 10000 Gadolinium (Gd) atoms [9].

These new high-sensitivity probes are commonly used to target endovascular biomarkers [such as ανβ3 integrins in tumor vessels, for example [6]], but their relatively high hydrodynamic size makes it difficult to use them for intra-cerebral biomarkers targeting. First, they are not able to naturally cross the blood–brain barrier (BBB) and reach cerebral tissues, and then, even if the BBB is passed through, their diffusion to targets can be considerably hindered because of their high molecular weight. Thus, design of such contrast agents must take into account the main properties of the media they will diffuse into.

For brain disease studies, one valuable information is the apparent diffusion coefficient (ADC) of the contrast agent in the extracellular space (ECS), which differs from the free diffusion coefficient (Dfree) owing to hindrance by cell membranes that impose tortuous paths to particle motion. From the measurements of ADC and Dfree, the ECS tortuosity can be computed to characterize this hindrance to contrast agent diffusion induced by cellular obstructions and then calibrate optimal injection doses and observation delay. Furthermore Thorne et al. have already shown that tortuosity values may be modified in some pathological brain tissues (for example after ischemia) [10].

Several methods were proposed to measure molecule diffusion through cerebral tissues. The first method implies the use of specific radiotracers perfused for several hours in the ECS of anesthetized animals [11-14]. The perfused region of the brain is then removed, frozen and sectioned. Brains of several animals are processed at various times after perfusion to obtain temporal evolution of radioactivity profile and determine radiotracer ADC. The post-mortem processing involved in this radiotracer technique represents its most important drawback.

The tetramethylamonium (TMA+) method is the most widely used today [15-18]. A defined release of TMA+ is delivered into the brain by iontophoresis technique using a micropipette. This ion remains predominantly in the ECS and does not alter physiological function. Its concentration is measured at a known distance from the release point by an ion-selective microelectrode. The advantage of the method is that micro-electrodes are small enough (tip diameter 2–12 µm) to avoid edema in the brain. The main drawback is that the ADC measure is based on concentration quantification at a single brain position.

A last technique, called integrative optical imaging (IOI), was presented in the last decade. It was developed by Nicholson and colleagues [10, 19] to determine in vivo the ADC and tortuosity of macromolecules tagged with fluorescent probes (dextrans or quantum dots) by epifluorescence microscopy. Compared with TMA+ technique, it allows 2D quantification of probe concentration, but only at the brain surface because of optical detection. These three methods are now well established and present almost the same results in term of estimated ADC and tortuosity of brain tissues.

The aim of the present study is to propose a methodology allowing in vivo concentration quantification of paramagnetic and superparamagnetic contrast agents (CAs), by acquiring dynamic MR relaxation time maps. We apply this method to estimate in vivo an ADC for five CAs with different values of dH injected into the rat brain. Taking advantage of MRI properties, we could overcome principal drawbacks of the three methods described earlier: the acquisition of 3D data enables in vivo diffusion information to be obtained in deep regions of the brain.

First, we parameterized T1 and T2 mapping sequences to quantify CA concentration with high sensitivity and sufficient spatio-temporal resolution. Then, in vitro experiments were performed on agar gels to set up a 2D diffusion model and estimate the free diffusion coefficient of the five different CA. Finally in vivo experiments were carried out: ADC values were measured after CA injection in the right caudate putamen of rats and we estimated the tortuosity into this brain region for each compound.


MR Contrast Agents

Table 1 summarizes the physicochemical properties and hydrodynamic diameters (dH from 1 to 170 nm) of five different CAs provided by Guerbet (Roissy Charles de Gaulle, France). Four of them are Gd-based molecules and belong to the family of paramagnetic CAs (Dotarem®, P846, P792 and the Gd-emulsion). They induce a decrease in both longitudinal and transverse relaxation times of surrounding water protons. At 7 T, this type of CA is often detected with T1 strategies [20-22], providing a better sensitivity than T2 approaches. The fifth CA (P904) is an USPIO consisting of an iron oxide core coated with hydrophilic polymers. The nonhomogeneous distribution of these superparamagnetic particles significantly decreases the measured spin–spin relaxation times (T2T2*) consecutively to an accelerated loss of spins phase coherence. This phenomenon is magnified at high magnetic field, which can explain why T2 and T2* strategies are commonly used at 7 T to detect and quantify such nanoparticles [23, 24].

Table 1. Relaxation properties (r1 and r2) at 7 T and hydrodynamic size (dH,ls assessed by light scattering) of the contrast agents used in the study
CATyper1 (m m−1 s−1)r2 (m m−1 s−1)dH,ls (nm)

Longitudinal r1 and transverse r2 relaxivities were measured in vitro at 7 T using galleries of tubes containing different concentrations of CA diluted in a 0.3% agar matrix, and maintained at physiological temperature (37 °C). Hydrodynamic diameters (dH,ls) were assessed by light scattering, except for Dotarem®, the small size of which prevents precise diameter estimation using this technique.

Mapping Sensitivity

Figure 1(a) represents a T1 map for several Dotarem® tubes and a T2 map for several P904 tubes. For Dotarem®, the sensitivity achieved with T1 strategy is better than 2.5 µ m in terms of Gd concentration (Fig. 1b). For P904, the T2 mapping sequence allows a detection threshold below 3.5 µ m of iron (Fig. 1c), which represents a nanoparticle concentration of less than 0.5 n m. These estimations of sensitivity were used to threshold and analyze concentration maps acquired during both in vitro and in vivo diffusion experiments.

Figure 1.

In vitro sensitivity of T1 and T2 mapping sequences. a) T1 (respectively T2) map of Dotarem® (respectively P904) at different concentrations of Gd (respectively Fe). b) T1 values with corresponding standard deviation in each Dotarem® tube. c) T2 values with corresponding standard deviation in each P904 tube.

In vitro Diffusion

For each contrast agent, free diffusion coefficient Dfree was determined in dilute agar gels at 37 °C from concentration maps obtained by relaxation time mapping. Considering the 2–3 mm depth chimney induced by the syringe needle at the injection site, we assumed a cylindrical symmetry for the experiment, leading us to consider a 2D model for the CA diffusion (Fig. 2).

Figure 2.

Contrast agent injection. a) In vitro in agar gel. b) In vivo in rat brain. Considering the 2–3 mm depth chimney induced by the syringe needle at the injection site, a cylindrical symmetry is assumed for the experiment.

Figure 3(a) shows a subset of estimated concentration maps and corresponding 2D Gaussian fits at different time points after injection for one Gd-chelate (P792). From these maps, diffusion coefficients DX and DY along the main axes of Gaussian function are extracted to compute free diffusion coefficient Dfree. As expected, this coefficient decreases with the size of the particle (i.e. DDotarem® > DP846 > DP792 > DP904; Table 2) and is in all cases isotropic (DX ≈ DY; Fig. 3b). At our imaging timescale (~1 h), the Gd-emulsion diffusion was highly restrained and could not be evaluated (DGd-e < 0.1 × 10−11 m2 s−1).

Figure 3.

In vitro diffusion of P792. a) Experimental concentration maps (top line) and respective fits with 2D Gaussian function (bottom line) at different time points (7 min, 21 min, 35 min and 49 min) after P792 injection in agar matrix. b) Estimation of DX and DY to determine the free diffusion coefficient Dfree. The temporal evolutions of the Gaussian function spreads along its main axes (math formula and math formula) are adjusted by a linear model which slopes correspond to DX and DY.

Table 2. Free diffusion coefficient (Dfree) measured in agar gels, hydrodynamic diameter derived from the Stokes–Einstein equation (dH,stokes), apparent diffusion coefficients (ADC) measured in vivo in the right caudate putamen, corresponding tissue tortuosity (λ) and characteristic diffusion time (Tdiff) for each CA. For Gd-emulsion, the experiment timescale was not sufficient to detect any in vitro or in vivo diffusion. Thus, hydrodynamic diameter, tortuosity and characteristic diffusion time could not be estimated (NE).
CADfree (× 10−11 m2 s−1)dH,stokes (nm)ADC (× 10−11 m2 s−1)λTdiff (min)
Dotarem®48.5 ± ±
P84615.5 ± ± 0.33.3311.9
P7929.8 ± ± 0.33.5020.8
P9043.2 ± 0.421.20.2 ± 0.14.0069.5

From the measured free diffusion coefficient, the hydrodynamic diameter of the CA could be estimated using the Stokes–Einstein equation [equation ((1))] verified for diffusion of spherical particles through liquid with low Reynolds number:

display math(1)

where k = 1.38 × 10−23 Pa m3 K−1 is the Boltzmann constant, T is the absolute temperature (in K) and η is the viscosity of the diffusion media. As the agar concentration was very low (0.3% w/w), the diffusion media was assimilated to pure water at 310 K (η = 6.92 × 10–4 Pa s). Hydrodynamic diameters estimated for each CA are summarized in Table 2 and are very close to those measured by light scattering (Table 1).

These results confirm that the hypothesis of a 2D diffusion model of spherical particles in pure water was fairly reasonable to obtain accurate information on free diffusion coefficients and hydrodynamic sizes of the CAs used in this study.

In vivo Diffusion

Figure 4(a) represents the overlay of anatomical images of rat brain with P792 concentration maps, revealing its diffusion through cerebral tissues during 2 h after injection. Each concentration map is fitted with a 2D-Gaussian function (Fig. 4b), and from the temporal evolution of Gaussian spreads along main axes, we extract diffusion coefficients DX and DY, and then determine the apparent diffusion coefficient of the CA (Fig. 4c).

Figure 4.

In vivo diffusion of P792. a) Overlay of anatomical images with P792 concentration maps at different time points after injection (34 min, 62 min, 90 min and 118 min). b) Experimental concentration maps (top line) and respective fits with 2D Gaussian function (bottom line). c) Estimation of DX and DY to determine apparent diffusion coefficient ADC. The temporal evolutions of the Gaussian function spreads along its main axes (math formula and math formula) are adjusted by a linear model which slopes correspond to DX and DY. d) Amount of contrast agent at the injection site over the time, determined by integration of the concentration map.

The CA concentration was integrated around the injection site and plotted as a function of time (Fig. 4d). The total amount of contrast agent was stable during the diffusion process, confirming that particles were not leaking through the vascular system. Additionally, if contrast agents were internalized into cells, a decrease in the total amount of particles would be observed, owing to relaxivity quenching [25]. Consequently this experiment confirms that contrast agents remain confined to the extracellular space after their intra-cerebral injection.

For all molecules, diffusion in cerebral tissues is clearly hindered compared with free diffusion in agar gels, resulting in ADC values approximately 10 times lower than respective Dfree (Table 2). Furthermore, as observed in vitro, ADC is directly correlated to CA hydrodynamic size (ADCDotarem® > ADCP846 > ADCP792 > ADCP904). Once again, our imaging protocol does not allow the quantification of the biggest probe diffusion (Gd-emulsion). Nevertheless, we notice that a significant diffusion remains detectable for a 22 nm particle (P904).

Values of Dfree and ADC estimated for each compound were then used to determine the corresponding tissue tortuosity λ (Table 2). Interestingly, λ slightly increased from 3.25 to 4.00 with the CA size, as already mentioned in previous studies [10, 19].

For the four CAs exhibiting significant diffusion at the experiment timescale, the time (Tdiff) necessary to diffuse along a characteristic distance between two capillaries in the brain (100 µm) [26] was calculated. This time varied from 3.6 to ~20 min for the Gd-chelates and was evaluated to be around 70 min for P904. After crossing the BBB, these four compounds can diffuse throughout the whole brain in a time compatible with in vivo molecular imaging experiments. To calibrate the optimal delay between injection and sequence acquisition, contrast agent binding features will have to be taken into account. The dissociation of the molecule to its specific biomarker must be significantly slower than its clearance rate through cerebral tissues.


Temporal and Spatial Resolution

The main objective of this study was to quantify the diffusion of CAs through different media. This implies an imaging protocol able to detect low and localized variations of CA concentration. A compromise between the accuracy on concentration quantification and the spatio-temporal resolution of the diffusion problem had to be determined. The different parameters of our methodology (acquisition time, voxel size) were optimized in order to measure precisely the diffusion of the smallest CA used in this study.

From the literature [10], the ADC of a 3 nm particle in the rodent cortex is D3nm ≈ 5 × 10−11 m2 s−1. We simulated a CA injection (2 μL, 1 m m) into a media with such diffusion coefficient (Fig. 5a), and we assumed that the first concentration measurement was performed 12.5 min after injection. Figure 5(b) represents the contrast agent concentration at the injection site as a function of time. We observed that CA concentration was halved after 25 min and quartered 50 min after injection. Considering these observations, an acquisition time of around 12.5 min was chosen to ensure a sufficient time sampling of diffusion process.

Figure 5.

Simulation of a CA injection (2μL, 1mM) into a media with a diffusion coefficient D3nm~5 × 10−11 m2s−1. a) Concentration maps at different time points after injection (12.5 min, 25 min, 37.5 min and 50 min). b) Temporal evolution of contrast agent concentration at the injection site.

The characteristic distance L covered by a molecule diffusing with a coefficient D during a time T can be estimated using the approximation L ≈ √DT. During the acquisition time Tacq (~12.5 min), a 3 nm molecule covered the characteristic distance L of ~200 µm. The spatial resolution of mapping sequences was then set to this value.

Mapping Sensitivity

Sensitivity to contrast agent concentration was evaluated for the two mapping sequences using these optimal parameters. For the T1 mapping sequence dedicated to Gd-based CAs, the sensitivity achieved in vitro was better than 2.5 µ m in terms of Gd concentration. This value represents a concentration around 100 p m in terms of nanoparticles for the Gd-emulsion (containing around 30 000 Gd atoms), which confirms that this type of CA is a high-sensitivity probe for molecular imaging experiments. The T2 mapping sequence used for P904 experiments exhibits an in vitro sensitivity better than 3.5 µ m in terms of iron concentration. Considering the amount of CA injected (m m range) for both in vitro and in vivo experiments, our two mapping sequences offer the opportunity to study small concentration variations (μ m range) and to precisely follow CA diffusion.

Limitations of the Method

Although our results seem relevant to previous studies performed using other techniques, some limitations remain with our quantification approach. Indeed, concentration maps derived from T1 and T2 maps cannot be considered as fully quantitative because of two main effects. First, one significant bias for concentration quantification is due to the partial volume effect, which was not taken into account. When injected directly in cerebral tissues, CAs will not diffuse through cells but remain in the extracellular space. For a fully quantitative study, a multi-compartmental approach would have to be performed, taking into consideration proton exchange rates between extracellular, intracellular and vascular compartments. Nevertheless, this bias is critical for absolute concentration quantification but has limited impact for quantification of diffusion processes, since concentration variations only (gradient and laplacian) appear in the model equations.

The second limitation is related to the indirect measure of CA concentration [equation ((5))], which requires an interaction model between CA molecules and surrounding protons (inner- and outer-spheres theory). Furthermore, the parameters of this model (r1 and r2 relaxivities) were measured in vitro (agar gel) at 37 °C. Despite an agar concentration adjusted to mimic cerebral tissues and measurement at physiological temperature, these values might slightly vary in biological tissues.

Free Diffusion Coefficient and Hydrodynamic Diameter

In vitro experiments performed in highly diluted agar gels allowed the measurement of free diffusion coefficients and then the deduction of hydrodynamic diameters of the different molecules using the Stokes–Einstein equation. They were consistent with dH values measured by light scattering. This method is based on intensity fluctuations of light scattered by particles under Brownian motion [27]. It turns out that the linewidth of the light-scattered spectrum is proportional to the particle diffusion coefficient. Hydrodynamic sizes are again derived from the Stokes–Einstein law. This method is widely used when molecule size exceeds 2–3 nm, whereas the hydrodynamic size of smaller particle is often derived from molecular modelling. This last method generally leads to an underestimation of hydrodynamic size since the hydration layer is not properly taken into account. With our direct measure of free diffusion coefficient, it appears that a large range of hydrodynamic sizes can be estimated.

Apparent Diffusion Coefficient and Tissue Tortuosity

In vivo experiments have shown the ability of CA with sizes up to 22 nm to diffuse through brain tissues. This is consistent with the approximate intercellular ECS spacing, which was estimated to be 20–50 nm [28, 29]. Moreover, no active pathway was found to allow the diffusion of the biggest particle through cerebral tissues. For the smallest contrast agents, the tortuosity derived from Dfree and ADC estimations did not significantly vary with the CA size. In this case, the Stokes–Einstein law seems to remain valid considering a correction factor of λ2 (Fig. 6).

Figure 6.

Diagram representing the apparent diffusion coefficient (ADC) of the contrast agents as a function of the inverse of their hydrodynamic diameter (dH,stokes). The Stokes–Einstein relation is verified in vivo.

Our estimated values of tortuosity are slightly higher than those reported from previous studies of nanoparticles diffusion in cortical structures. Because we injected CA in deeper regions, this difference may reflect different tissue properties between cortex and caudate putamen. The other explanation could result from the delivery method of CA to the brain. The 0.5 mm injection needle may cause hemorrhage, inflammation or edema in surrounding tissues, which may modify some assumptions or parameters of the tortuous diffusion model. It has already been reported that diffusion is clearly hindered in tissues with edema [30], and tortuosity found in the case of damaged tissues corresponds to the values measured in our study.

Solutions to this limitation have to be investigated. One can propose the use of a smaller injection needle (micro-injectors), but the most promising tool is probably i.v. injection after a focal opening of the BBB induced by ultrasound sonication of microbubbles [as first proposed by Hynynen et al. [31]]. In addition to avoid edema, this method would allow a controlled delivery of CA at specific brain locations. Coupled to our 3D methodology, a noninvasive estimation of diffusion processes could be assessed for different tissue properties.

Finally, our results represent valuable information in fields far beyond molecular imaging. For example, the characteristic hydrodynamic sizes of recombinant adeno-associated virus vectors injected for gene therapy are typically around 20 nm [32]: their diffusion through cerebral tissues may be estimated using our experimental data on P904.


In this study, we presented a methodology based on quantitative MRI acquisitions, to precisely assess CA concentration after injection and follow its diffusion in both in vitro and in vivo conditions. The results provide accurate data on probe hydrodynamic sizes and tissues tortuosity, as well as an estimation of characteristic diffusion time in rat brain. These findings are valuable information for the design of molecular probes and calibration of molecular imaging experiments.


Magnetic Resonance Imaging

MRI experiments were performed on a 7 T Pharmascan scanner (Bruker, Ettlingen, Germany) with a 90 mm inner diameter and equipped with a 750 mT m−1 gradient insert. A 3 cm-diameter birdcage 1 H coil was used for in vitro and in vivo imaging. According to the type of contrast agent, either a T1 (for Gd-based CA) or a T2 (for P904) mapping sequence was acquired to quantitatively follow CA concentration after injection.

The T1 mapping sequence consisted of a segmented series of fast gradient echo images acquired at different time points after magnetization inversion, in order to follow the entire T1 recovery curve [33]. Sequence parameters were: repetition time (TR1) = 5 ms, echo time (TE) = 2.5 ms, six segments, flip angle = 5°, matrix = 128 × 104 × 14 and resolution = 0.225 × 0.225 × 1 mm3. Sixty inversion times TIs (from 45 to 5000 ms, spaced by ΔTI = 85 ms) were used to optimize the accuracy on T1 measure. Repetition time between the acquisition of two segments was TR2 = 9 s and total acquisition time was 14 min (including image reconstruction time).

The T2 mapping sequence was a multi-slice–multi-echo (MSME). Sequence parameters were: TR = 3000 ms, 36 echoes (from 8.3 to 300 ms, spaced by ΔTE = 8.3 ms), matrix 144 × 117 × 9, resolution = 0.2 × 0.2 × 1 mm3, number of experiments = 2, acquisition time = 12 min.

In order to realign the pre- and post-injection volumes, an anatomical image with high spatial resolution was acquired. An inversion–recovery turbo spin echo (IR-TSE) sequence was used with the following parameters: TR = 3300 ms, turbo factor = 8, TEeff = 38.5 ms, TI = 550 ms, matrix = 192 × 156 × 35, resolution = 0.15 × 0.15 × 0.4 mm3.

In vitro Experiments

All experiments were carried out at physiological temperature (37 °C) using an air heater device and a temperature probe inside the magnet. The sensitivity of the T1 mapping approach was estimated on a gallery of tubes containing Dotarem® at different concentrations (10/5/2.5/0 μ mGd), while the sensitivity of the T2 mapping strategy was evaluated on a gallery of tubes containing P904 at different concentrations (70/7/3.5/0 μ mFe).

In vitro diffusion experiments were then performed on agar gels (0.3% w/w), an obstacle-free medium simulating in vivo relaxivities [10]. A 5 μL aliquot of CA (10 m m Dotarem®, 2.5 m m P846, 10 m m P792, 2.5 m m Gd-emulsion and 1 m m P904) was injected using a Hamilton syringe held in a stereotactic frame, and its diffusion was followed for approximately 1 h. Relaxation time maps were acquired on a single slice centred on the injection site, resulting in reduced acquisition time for the T1 mapping sequence (7 min).

Animal Preparation

In this study, all experimental procedures were performed in strict accordance with the recommendations of the European Community (86/609) and the French National Committee (87/848) for care and use of laboratory animals. Ten male rats (125–150 g, Sprague–Dawley, Janvier, Le Genest-St-Isle, France) were used for the experiments (n = 2 for each compound). The first MRI session was performed on each animal to acquire anatomical images and baseline relaxation time maps. To proceed to the intra-cerebral CA injection, rats were anesthetized with an intra-peritoneal injection of a drug cocktail (ketamine–domitor, 0.6 mL/100 g) and placed in a prone position into a stereotactic frame with ear and bite bars. A small part of the skull was removed with a 1 mm milling machine: the aperture was drilled 0.5 mm ahead and 2 mm to the right of the bregma, chosen as an anatomical landmark. A 2 μL aliquot of CA (at the same concentrations as for in vitro experiments) was then injected with the Hamilton syringe at a depth of 2.5 mm from the top of the brain, which corresponds to an injection site located into the right caudate putamen. The second MRI session started approximately 30 min after CA injection, and lasted around 1.5 h to follow CA diffusion (acquisition of six relaxation time maps).

For MRI sessions, rats were maintained anesthetized in a stereotactic headset with a mix of isoflurane (0.5%), air and oxygen. Body temperature was continuously monitored using a rectal probe and kept at around 37 °C using an air heater device. Respiration was also controlled throughout the experiment in order to maintain the animal below 75 respirations per minute.

Data Analysis

Data analysis was performed using Matlab routines (MathWorks, Natick, MA, USA). Raw data were first reconstructed using a homemade pipeline. Then T1 and T2 maps were generated from T1 and T2 mapping sequences using suitable models. T1 maps were obtained using the approach proposed by Deichmann and his colleagues [33-36]. Measured longitudinal magnetization (M) was fitted pixel by pixel as a function of the TI using the following equation:

display math(2)

From A, B and T1* values, T1 was then determined using the relation:

display math(3)

T2 maps were generated from the MSME sequence by fitting the transverse magnetization (M) measured for different TEs with a T2 decay function [37]:

display math(4)

Pre- and post-injection imaging volumes had to be realigned because the animal was taken out of the MRI scanner for CA intra-cerebral injection. To estimate realignment parameters, high-resolution anatomical images were acquired before and after injection. First, brain masks were manually generated on the two sets of images, and a smoothing Gaussian filter was applied to decrease side effects. Then, the realignment algorithm implemented in SPM5 (Wellcome Trust Centre for Neuroimaging, London, UK) was used to co-register the two volumes using six rigid transformations. These transformation parameters were finally applied to the relaxation time map acquired before injection to realign it on the series of relaxation time maps acquired after injection.

CA concentration maps were calculated from the realigned T1,0 (respectively T2,0) map and the T1 (respectively T2) maps after injection using the following equation [38], considering that relaxivity r1 (respectively r2) measured in vitro in agar matrix hardly differs from the one in rat brain:

display math(5)

To estimate a diffusion coefficient from the dynamic series of concentration maps, the hypothesis of a 2D diffusion process in a homogeneous or tortuous environment without source term was made. The solution to this diffusion problem leads to fitting, at each acquisition time point, of the CA concentration map with the following 2D Gaussian function:

display math(6)

where A is an amplitude term and (x0, y0) the center of the Gaussian function. The parameters a, b and c are defined as functions of Gaussian spreads (σX and σY) along its main axes (X and Y), and the angle θ of the spot with absolute axes (x and y):

display math(7)

From the spreads σX and σY of the Gaussian function determined at each acquisition time point t, the diffusion coefficients along main axes (DX and DY) were estimated using the following relationships:

display math(8)

The free and apparent diffusion coefficients (Dfree and ADC) of the injected CA are then defined as:

display math(9)

Considering the composition of brain extracellular space, the in vivo diffusion process should be considered as hindered by cells instead of occurring in an obstacle-free medium. This hindrance relatively to a free medium is usually quantified introducing the tissue tortuosity λ [39]:

display math(10)


This work was part of the Iseult/INUMAC project, supported by the French public agency OSEO dedicated to the support of small and medium-sized companies.